I've been using Squarespace on this site for about 6 weeks after using Wordpress (self-hosted on Godaddy and .com) for several years. There are some big differences between the two platforms, and each is better suited for different tasks and types of users. Here are my thoughts on Squarespace vs Wordpress and what type of user should go with each platform.
Wordpress is powerful but requires maintenance
Wordpress powers many of the web's most popular blogs and news sites. There are a few incarnations of Wordpress that are controlled by different entities. Wordpress.com offers free accounts with several limitations and up-sells features. Wordpress.org offers the software free and open source, and several web hosts use it to offer hosting packages with easy installation.
A Wordpress.com site is relatively easy to operate from a technical perspective but can get expensive when purchasing lots of additional features. Running a self-hosted Wordpress site can be very affordable (I run 3 sites on a $9 per month 'unlimited' hosting plan) but requires a greater degree of technical sophistication, maintenance, and willingness to get your hands dirty.
On a self-hosted site, it's up to you to keep the various pieces of software you run (Wordpress, themes, plugins) up to date, test them all for compatibility, and regularly back up your site. If you run into problems there's no support line to call. You have to rely on volunteers on the Wordpress.org support forums or hire a Wordpress expert. I have had issues that required troubleshooting by manually overwriting files on my server over FTP and took my site down for several days.
Some web hosts offer fully managed Wordpress packages that handle maintenance and offer support, but they are more expensive and may have traffic limits.
The open nature of Wordpress is both a strength and a weakness. It's great that there is a large community of developers building interesting plugins and themes for the platform, but everything doesn't always work as it should and getting support can be a challenge.
Squarespace makes my life easier
Operating a Squarespace site is a much simpler experience overall. They control all of their own software, so compatibility isn't an issue. They handle updates and backups, and there is a dedicated support team if you do run into a problem. I had a few questions when setting up my site and most were answered very quickly, but one was deemed to require premium support and an additional fee. There was nothing wrong with the SS software, I just preferred it behaved an alternate way.
Squarespace also has a powerful WYSIWYG (what you see is what you get) website editor which makes it easy to create a nice looking site for a variety of purposes and layouts, whereas Wordpress is more focused on a traditional blog/news format. Squarespace has several nice built-in tools that I use to link to Amazon products, create signup forms for my mailing list, and more. However, they are missing some tools I had grown used to using on Wordpress and there is no such thing as a 3rd party plugin on Squarespace.
Squarespace vs Wordpress and Godaddy
In many ways Apple vs Android is an apt comparison to Squrespace vs Wordpress. Wordpress is great for people that want to dig in and don't mind occasionally breaking things, where Squrespace is overall easier to setup and use and more or less works as advertised.
Squarespace works well as a general purpose website builder and is ok as a basic blogging platform. I would tend to recommend it to people that don't want to worry about maintaining a website weekly/monthly, such as restaurants, small businesses, artists, part-time bloggers, etc.
Wordpress is much more powerful as a blogging or content management platform, but requires more technical sophistication and maintenance. I'd recommend it to people building a professional blog or news site that are comfortable diving into it or have access to developers. If you like the idea of Wordpress but don't want to deal with the maintenance, look into Wordpress.com or a managed Wordpress hosting plan.
Squarespace is a bit more expensive than my self-hosted Wordpress sites, but it saves me time and I like having a dedicated support line if something goes wrong. As someone who isn't a designer or know CSS, I appreciated the visual editor. I plan to continue using Squarespace for this site and Wordpress to run some smaller sites and prototype new ideas.